Differential and Integral Equations

Modified motion by mean curvature: local existence and uniqueness and qualitative properties

A. Bonami, D. Hilhorst, and E. Logak

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Abstract

We consider some free boundary problems involving motion by mean curvature and a nonlocal term. They arise as singular limits of various phase transition models. Using precise regularity estimates in Hölder spaces, we prove that these problems are well-posed. We study the qualitative behavior of the motion law and show in particular that the inclusion of interfaces is not preserved in time.

Article information

Source
Differential Integral Equations Volume 13, Number 10-12 (2000), 1371-1392.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356061130

Mathematical Reviews number (MathSciNet)
MR1787072

Zentralblatt MATH identifier
0994.35053

Subjects
Primary: 35K55: Nonlinear parabolic equations
Secondary: 35A07 35B65: Smoothness and regularity of solutions 35R35: Free boundary problems 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)

Citation

Bonami, A.; Hilhorst, D.; Logak, E. Modified motion by mean curvature: local existence and uniqueness and qualitative properties. Differential Integral Equations 13 (2000), no. 10-12, 1371--1392. https://projecteuclid.org/euclid.die/1356061130.


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